1. Field of the Invention
The present invention relates to a method to determine a feedforward transfer function of a control system in a lithographic apparatus, a lithographic apparatus and a method for manufacturing a device.
2. Description of the Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
As an example, in a so called step and scan lithographic apparatus, both reticle stage and wafer stage perform step- and scan moves at nanometer scale accuracy. Throughput demands require high velocity and acceleration levels. These high acceleration levels may be conflicting with a demand for position accuracy as dynamics of the stages are excited during acceleration phases. Vibrations need to settle in a certain settling time before exposure can begin. To address these needs, sophisticated motion control is used to control 6 degrees of freedom (6 DOF) of mechanics of both reticle- and waferstage. Feedback control is used to guard stability and improve disturbance rejection, while feedforward control is used to achieve the desired tracking performance.
In the past years, iterative learning control has been considered to determine a feedforward signal in controlling a position related quantity (such as a position, a velocity, a jerk, etc) of a stage (such as a substrate stage or a reticle stage) of a lithographic apparatus. In a combined feedforward/feedback control system, iterative learning control provides for a learning of the feedforward signal by providing a setpoint stimulus to the control system, applying an initial or previously determined feedforward signal, measuring an error signal expressing a difference between a desired response of the stage and a measured or obtained response of the stage, and determining a following or subsequent feedforward signal from the error signal and the feedforward signal as applied. This process may be repeated iteratively, until a number of iterations has been achieved, or any other suitable criterion has been met, such as a convergence of the feedforward signal, a magnitude or norm of a remaining error signal, etc. Thus, in iterative learning control, an update is made to the feedforward signal off-line based on a measured error signal. After a few trials (iterations) a stable ILC converges to an ideal feedforward signal, which provides an ability to remove or at least reduce a repetitive tracking error.
Despite benefits that may be provided by application of iterative learning control, a limitation of it may be that such learned signal only holds for a particular setpoint (e.g. a setpoint versus time pattern corresponding to a stage movement pattern), being the setpoint that has been applied during the iterative learning. When the setpoint changes, system dynamics are excited differently. It is considered too time consuming, or even impossible to learn every possible occurring setpoint profile, because variations may be so numerous that almost infinitely many setpoint profiles may occur. This aspect is even aggravated in multi input, multi output systems, as there, a variety in setpoint profiles may increase as compared to a single input, single output system. Thus, it would be desirable to use the learned information from a limited amount of learned setpoints.